Question

If there is a loss of 40% when a good is sold at ${\displaystyle \frac{2}{5}}th$ of its earlier selling price. Find the profit% after selling the goods at an earlier selling price?

Answer 1

Hint: Start by taking the selling price as x for both the conditions stated in the question. Try to form the relation between the two selling prices as stated in the question and apply the loss(%) formula in order to get one of the unknown values and use the relation to find the other one . Apply the profit(%) formula to get the final desired value.

Complete step-by-step answer:
Given, loss of 40% at selling price${\displaystyle \frac{2}{5}}th$ of earlies selling price.
Let , the first selling price be =$x_1$
Then , second selling price be =$x_2$
$\therefore x_2={\displaystyle \frac{2}{5}}{x}_1\to (1)$
We know , $\text{Loss}(\mathrm{\%})={\displaystyle \frac{\text{Cost price - selling price}}{\text{Cost price}}}\times 100$
$$\begin{gathered} 40={\displaystyle \frac{\text{C}\text{.P}\text{. - }{x}_2}{\text{C}\text{.P}\text{.}}}\times 100 \\ \Rightarrow {\displaystyle \frac{40}{100}}={\displaystyle \frac{\text{C}\text{.P}\text{. - }{x}_2}{\text{C}\text{.P}\text{.}}} \\ \Rightarrow 0.4=1-{\displaystyle \frac{x_2}{\text{C}\text{.P}\text{.}}} \\ \Rightarrow {\displaystyle \frac{x_2}{\text{C}\text{.P}\text{.}}}=1-0.4 \\ \Rightarrow {\displaystyle \frac{x_2}{\text{C}\text{.P}\text{.}}}=0.6 \\ \Rightarrow x_2=0.6\times \text{C}\text{.P}\text{.} \end{gathered}$$
Now , substituting this value in relation 1, we get
$$\begin{gathered} x_2={\displaystyle \frac{2}{5}}{x}_1 \\ 0.6\times \text{C}\text{.P}\text{. = 0}\text{.4}\times x_1 \\ \Rightarrow x_1=1.5\times \text{C}\text{.P}\text{.} \end{gathered}$$
Now, we know $\text{Profit}(\mathrm{\%})={\displaystyle \frac{\text{selling price - Cost price}}{\text{Cost price}}}\times 100$
Profit earned while selling at first selling price,
$$\begin{gathered} \text{Profit}(\mathrm{\%})={\displaystyle \frac{\text{1}\text{.5}\times \text{C}\text{.P}\text{. - C}\text{.P}\text{.}}{\text{C}\text{.P}\text{.}}}\times 100 \\ \Rightarrow \text{Profit}(\mathrm{\%})=(1.5-1)\times 100 \\ \Rightarrow \text{Profit}(\mathrm{\%})=(0.5)\times 100 \\ \therefore \text{Profit}(\mathrm{\%})=50\mathrm{\%} \end{gathered}$$
Therefore , the profit earned is 50% when sold at an earlier price.

Note: All the formulas related to profit and loss must be well known to the students . Attention must be given while substituting the values in the equation and also while forming the required relations.
Always remember if you get profit as negative value , then it is a loss and not a profit.